Outlook 2003 is not automatically underlining incorrect spelling in red like Microsoft Word does.
This worked for me but there are other things to try as well:
Open up Outlook and click tools
Click Options
Select the mail format tab
Check the box beside "Use Microsoft Word to edit e-mail messages..."
Click Apply Changes
Other things to try
Check Outlook for updates
Open a new message, hit f7, select spelling and grammar options, ensure check spelling as type is selected
In Outlook select Help > About > Disabled Items > and ensure spell check is not listed
Spell check won't correct the signature file, so if the email is being written in the sig file the email will not be spell checked
This worked for me but there are other things to try as well:
Other things to try